Question

A hydrate of $N{a_2}S{O_3}$ has $50\%$ water by mass. It is:
A.$N{a_2}S{O_3}.4{H_2}O$
B.$N{a_2}S{O_3}.6{H_2}O$
C.$N{a_2}S{O_3}.7{H_2}O$
D.$N{a_2}S{O_3}.2{H_2}O$

Answer 1

You just need to find the ratio of number of moles of given substance of the compound to the water of crystallization. Hence you will find the number of water molecules attached.
Formula used: The formula used in the above question is ${\text{number of moles = }}\dfrac{{{\text{given amount of substance}}}}{{{\text{total amount of substance}}}}$

Complete step by step answer:
Here in the given question the ratio of $N{a_2}S{O_3}:{H_2}O$ is $50:50$ by mass.
In which $N{a_2}S{O_3}$ has a molecular mass of $126$ and ${H_2}O$ has a molecular mass of $18$.
Hence the ratio of number of moles becomes $\dfrac{{50}}{{126}}:\dfrac{{50}}{{18}}$
And therefore, the ratio of number of moles becomes $1:7$ . which means one molecule of $N{a_2}S{O_3}$ combines with seven molecules of ${H_2}O$ .
Hence the compound thus formed is $N{a_2}S{O_3}.7{H_2}O$.
Therefore the correct option is option ( C ) .

Additional Information:
Moles: A mole is nothing but simply a unit of measurement. A mole is the quantity of anything which has the exact same number of particles that are found in $12grams$ of $carbon - 12$ . That number of particles is Avogadro’s number of particles, which is roughly $6.022 \times {10^{23}}$ .
Molarity: Molarity of a substance is defined as the moles of solute per litres of a given solution. Molarity can also be defined as the molar concentration of a solution.

Water of crystallization: Water of crystallisation are the water molecules which are chemically bonded into a crystal structure. Water of crystallisation is separated from the main compound by a dot.
N{a_2}S{O_3}.7{H_2}O$$$$ \leftarrow water of crystallisation
Hydrated compound means that the given solid crystals contain water of crystallisation.
Dehydration means the removal of water of crystallisation.
no water of crystallisation means an anhydrous substance.

Note:
Water of crystallization or water of hydration are water molecules that are present inside crystals. Water is often incorporated in the formation of crystals from aqueous solutions.